1. Field of the Invention
This invention generally relates to an active filter type signal adjusting circuit used to adjust the frequency characteristics of an electric circuit and, more particularly, to an active filter type signal adjusting circuit used for adjusting the image quality of a video signal processing circuit.
2. Description of the Related Art
A conventional frequency characteristics adjusting circuit shown in FIG. 1 is applied to video equipment as an image quality adjusting circuit. This circuit is a so-called active filter type signal adjusting circuit. An input signal is supplied to the first input terminal (+) of first operational amplifier op1 and the second input terminal (-) of third operational amplifier op3. An output from first operational amplifier op1 is supplied to one terminal of first capacitor C1 and the first input terminal (+) of second operational amplifier op2. Note that the other terminal of first capacitor C1 is grounded in an AC manner. An output from second operational amplifier op2 is fed back to the first input terminal (+) of first operational amplifier op1 through second capacitor C2 and is supplied to buffer amplifier BF. An output from buffer amplifier BF appears at an output terminal and is supplied to the second input terminals (-) of first and second operational amplifiers op1 and op2 and the first input terminal (+) of third operational amplifier op3.
In the above circuit, voltage-current conversion coefficient gm3 of third operational amplifier op3 is adjusted, so that gain control having a predetermined angular frequency as a center frequency can be achieved.
Output currents I1, I2, and I3 from operational amplifier op1, op2, and op3 are defined as: EQU I1={x(S)-Y(S)}gm1 EQU I2={I1.times.(1/SC1)-Y(S)}gm2 EQU I3={Y(S)-X(S)}gm3
wherein gm1, gm2, and gm3 are voltage-current conversion coefficients of operational amplifiers op1, op2, and op3, X(S) (where S is a product of imaginary unit j and angular frequency .omega. [S=j.omega.]) is an input signal, and Y(S) is an output signal which is given by: EQU Y(S)=X(S)+(I2+I3).times.1/SC2
When the above equations are arranged about X(S) and Y(S), the following input/output relationship can be obtained: EQU Y=X+[{(X-Y)(gm1/SC1)-Y}gm2+(Y=X)gm3].times.(1/SC2) (1)
Therefore, transfer function H(S) of the frequency characteristics (to be referred to as f-characteristics) adjusting circuit is as follows: ##EQU1## Coefficient gm3 is changed to adjust the gain characteristics, so that the f-characteristics adjustment represented by three curves ( .circle.1 , .circle.2 , and .circle.3 ) in FIG. 2 can be realized.
Equation (2) derives gain characteristics G(.omega.) and group delay characteristics .tau.(.omega.), as defined in the following equations (3) and (4): ##EQU2##
In order to realize the gain through characteristics of this circuit which are represented by curve .circle.2 in FIG. 2 in an adjusting mode, the following condition must be realized. If G(.omega.).tbd.1 in equation (3), the solution for satisfying this condition is as follows: EQU gm3=(1/2)gm2 (5)
This can easily be realized. Note that the denominator and numerator in equation (2) are conjugate complex numbers under the condition as defined by equation (5).
Even if equation (5) is substituted in group delay characteristics equation (4), only the following equation is given: ##EQU3## Therefore, through characteristics .tau.(.omega.).tbd.0 concerning the group delay cannot be realized.
In the conventional f-characteristics adjusting circuit as described above, coefficient gm3 is given by: EQU gm3=(1/2)gm2
Thus, the following problem is imposed. "Through characteristics can only be realized in gain, and f-characteristics are only realized in group delay."
This problem is caused by achieving the gain through characteristics of the conventional circuit under the condition that the denominator and numerator of the transfer function are conjugate complex numbers.
More specifically, the transfer function including denominator and numerator which are conjugate complex numbers is defined as: EQU H(.omega.)={f(.omega.)+jg(.omega.)}/{f(.omega.)-jg(.omega.)}
The gain characteristics thereof are given by: EQU G(.omega.)=.sqroot.[{f(.omega.)}.sup.2 +{g(.omega.)}.sup.2 ]/[{f(.omega.)}.sup.2 +{-g(.omega.)}.sup.2 ]
=1
Thus, the gain through characteristics can be realized.
Phase characteristics are defined as: ##EQU4## In addition, group delay characteristics obtained by the differential of the phase characteristics by an angular frequency are defined as: ##EQU5## wherein f'(.omega.) and g'(.omega.) are functions obtained by differentials f(.omega.) and g(.omega.) as a function of .omega.. Therefore, the group delay through characteristics cannot generally be obtained.
As has been described above, the perfect through characteristics of the f-characteristics adjusting circuit cannot be adequately achieved in the circuit shown in FIG. 1 by only the condition that "the denominator and numerator of the transfer function are conjugate complex numbers".
Therefore, an f-characteristics adjusting circuit is required which can realize a transfer function for achieving perfect through characteristics H(S)=1 as gain characteristics G(.omega.).tbd.1 and group delay characteristics .tau.(.omega.).tbd.0 during a "through" operation.